Potentially yes.
The breeding stock comes from a carefully selected and necessarily inbred line of bees which have then been exported ( further narrowing the base genetics )to an isolated area in NZ, then multiplied hugely,
With respect, I think you've misunderstood the purpose of any breeding programme, commercial or amateur, large scale or small scale. It is to concentrate genetics through active selection such that the favoured characteristics appear predictably, certainly more often than not, in the offspring. Breeding requires a degree of inbreeding in order to concentrate the favoured characteristics. Moving selected colonies to an isolated mating area is no different in outcome than purging non-conformant stocks from your own area to leave just the favoured ones; the net result of either is that the area is flooded/dominated/biased with the types of bees that you want to mate together.
presumably being open mated to fairly closely related drones.
I don't know how the outfit in question operates; ITLD may be able to provide more details. If inbreeding were becoming problemmatic in any breeding/raising/mating set-up then this would be obvious in poor quality mated queens, not least in aspects of brood survival, loss of vigour, and disease susceptibility.
I'd say it's wrong to assume that they are mated with closely related drones - it may be that they are purposefully mated with another selected line in isolation from their own line, in order to produce hybrid vigour. Again, the small scale 'local' bee improvement approach of dominating the area with favoured stocks, requeened from previous queen raising, also raises the very real possibility of mating with closely related drones.
Does raising thousands of queens from each breeder in this system make me wonder if there might be problems down the road ? of course.
The position in the US, where most of the stocks can reportedly be traced back to a handful of breeding outfits, and hence much genetic diversity has been lost, is concerning. However I do not see how this is paralleled by Murray's importation of queens. If everyone in his region was importing from this same queen producer, then yes, that could be a problem, just as it would if those same beekeepers were all getting their stock of 'pure' Amm from a single UK breeder. Indeed you could argue that an Amm-only stance for the UK would drastically reduce the genetic diversity from its current level, potentially losing a raft of positive options. I know the IoW disease is a prickly subject for the Amm fraternity, but it is a very real example of a closed population poorly placed to deal with a disease which its close relatives could withstand.
I'm afraid you appear to be critical of this breeding effort because it is done on a large scale, not because of the quality of the operation or of the resulting queens. Perhaps I have misunderstood your replies, but "big is bad" is not a constructive argument